Stat 432: Homework 5
1. In a different game of chance involving two fair dice, one die is rolled and the
number on the upper face is noted. A second die is rolled repeatedly until the sum of
the two dice is 4 or 7.
a. What is the probability that the game ends with a 4?
b. What is the probability that the game ends with a 7?
c. What is the probability that the game never ends?
2. Consider a similar game to the one in problem 1 only this time the second die is
rolled repeatedly until the sum of the two dice is 4 or 5.
a. What is the probability that the game never ends?
b. What is the probability that the game ends with a 4 given that the game ends?
3. The service time for a person calling into a call center is a continuous random
variable with a mean of 5 minutes and a standard deviation of 5 minutes. Service
times are assumed to be independent from call to call.
a. Suppose the number of calls to the call center, N, is a Poisson random variable
e 4 (4) n
n  0, 1, 2,  ). What are the mean and
n!
standard deviation for the total service time?
b. Suppose the number of calls to the call center, N, is a geometric random variable
with mean 4 (i.e. p N n  
with p = 0.2 (i.e. p N n   0.21  0.2n 1 n  1, 2,  ). What are the mean and
standard deviation for the total service time?
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